Multilevel panel data with time-invariant estimator: xtreg or melogit?

[Yixi Chen]

I have a panel dataset at weekly level. The dependent variable is whether a company spoke out at a given week (1=yes, 0=no). IV: historical slavery percentage at the company's local headquarter county (county level and time-invariant). Different companies can be nested within the same county. I also have state and industry information for each firm. Because the IV is time-invariant and at a higher level than my DV, xtreg, fe would not work. I used below model specification by adding state, industry, and week as dummies instead. Would it be the same as having state, industry, and week fixed effect?

xtreg dv iv controls i.industry i.week i.state, vce(cluster gvkey)

Alternatively, I used melogit to run multi-level model. However, they yield different results as the above xtreg model. Which one is more suitable given my multi-level data structure?

melogit dv iv  controls i.week ||industry:  || state: , cov(un)

[Carlo Lazzaro]

Yixi:
with a categorical dependent variable, -xtlogit- should be considered.
If you go -fe-, -State- and -industry- if, as expected, time-invariant, will be wiped out.
That said, going -re- if -fe- is the way to go (despite its aforementioned nuisances) would make your results inconsistent.

[Maarten Buis]

Not being able to answer the research question is more than just a nuisance; it is the end of that research question.

You should remember that all research (including research using fixed effects estimators) is fundamentally flawed. All we can do is the best we can and document any limitations. Random effects are no more inconsistent than regular linear regression. Fixed effects models are cool when they help, but when they don't you'll just do what you have to do.